Reformulation of Global Constraints

Author:

Nina Narodytska

School:

University of New South Wales

Supervisors:

Toby Walsh

George Katsirelos

Maurice Pagnucco

Abstract:

This dissertation is dedicated to the design and analysis of algorithms for global constraints.
Global constraints are one of the major contributors to the success of modern constraint
solvers in solving combinatorial and industrial problems. They serve as natural building
blocks in themodelling stage providing the user with a rich declarative language for problem
specification. Global constraints can also lead to dramatic reduction of the search space
during problem solving because their propagation algorithms leverage global knowledge
about the problem.

In this work we study a number of useful global constraints, including SEQUENCE,
ALL-DIFFERENT, GCC, GRAMMAR and NVALUE. We propose reformulations of these
constraints into logically equivalent problems on graphs or into logically equivalent sets
of primitive constraints. We analyse existing filtering algorithms for these constraints and
prove that our reformulations can simulate filtering algorithms for all these constraints with
a slight complexity overhead in some cases. These reformulations have a number of advantages;
in particular, they allow adding global constraints to a constraint solver without
implementing special-purpose filtering algorithms, they guarantee maintaining standard
consistency levels for propagation, and their time complexity is similar to or the same as
the best known special-purpose filtering algorithms. Finally, we investigate limitations of
our approach and show that for some constraints and their filtering algorithms a polynomial
size reformulation is not possible.